4. Find the equation of a line parallel to x-axis and passing through the origin.

Answers (1)

Equation of a line parallel to the x-axis and passing through the origin (0,0,0) is itself x-axis.

So, let A be a point on the x-axis.

Therefore, the coordinates of A are given by (a,0,0), where a\epsilon R.

Now, the direction ratios of OA are (a-0) =a,0 , 0

So, the equation of OA is given by,

\frac{x-0}{a} = \frac{y-0}{0} = \frac{z-0}{0} 

or  \Rightarrow \frac{x}{1} = \frac{y}{0} = \frac{z}{0} = a

Thus, the equation of the line parallel to the x-axis and passing through origin is 

\frac{x}{1} = \frac{y}{0} = \frac{z}{0}

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